Root systems and the Atiyah-Sutcliffe problem

@article{Malkoun2019RootSA,
  title={Root systems and the Atiyah-Sutcliffe problem},
  author={Joseph Malkoun},
  journal={Journal of Mathematical Physics},
  year={2019}
}
  • J. Malkoun
  • Published 28 February 2019
  • Mathematics
  • Journal of Mathematical Physics
In this short note, we show that the Atiyah-Sutcliffe conjectures for $n = 2m$, related to the unitary groups $U(2m)$, imply the author's analogous conjectures, which are associated with the symplectic groups $Sp(m)$. The proof is based on the simple fact that the root system of $U(2m)$ dominates that of $Sp(m)$. 
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8 References

Configurations of Points and the Symplectic Berry-Robbins Problem

We present a new problem on configurations of points, which is a new version of a similar problem by Atiyah and Sutcliffe, except it is related to the Lie group Sp(n), instead of the Lie group U(n).…

Configurations of points

  • M. Atiyah
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2001
Berry & Robbins, in their discussion of the spin–statistics theorem in quantum mechanics, were led to ask the following question. Can one construct a continuous map from the configuration space of n…

Surjective Linear Maps Between Root Systems with Zero

Abstract If R 1 and R 2 are root systems and there is a linear map which maps R 1 ∪{0} onto R 2∪{0} we write R 1 —> R 2. We determine all pairs (R 1, R 2) of irreducible root systems such that R 1 —>…

The geometry of point particles

  • M. AtiyahP. Sutcliffe
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 2002
There is a very natural map from the configuration space of n distinct points in Euclidean 3–space into the flag manifold U(n)/U(1)n, which is compatible with the action of the symmetric group. The…

Indistinguishability for quantum particles: spin, statistics and the geometric phase

  • M. BerryJ. Robbins
  • Physics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1997
The quantum mechanics of two identical particles with spin S in three dimensions is reformulated by employing not the usual fixed spin basis but a transported spin basis that exchanges the spins…

Edinburgh Lectures on Geometry, Analysis and Physics

These lecture notes are based on a set of six lectures that I gave in Edinburgh in 2008/2009 and they cover some topics in the interface between Geometry and Physics. They involve some unsolved…

The geometry of classical particles , Surveys in differential geometry , 1 - 15 , Surv

  • 2000

The geometry of classical particles, Surveys in differential geometry, 1 - 15

  • Surv. Differ. Geom.,
  • 2000